CN108106826A - The method of quick tracking frequency in During Fatigue Damage Process - Google Patents
The method of quick tracking frequency in During Fatigue Damage Process Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
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- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
- G01M5/0066—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by exciting or detecting vibration or acceleration
Abstract
The present invention relates to a kind of methods of quick tracking intrinsic frequency during fatigue test of structure, frequency response function variation before and after the method analysis structural damage, the relation between frequency response function variation and intrinsic frequency variation is therefrom found, the method for realizing intrinsic frequency tracking is found with this.
Description
Technical field
The present invention relates to structural damage dynamic characteristic test technical field, be specially in a kind of During Fatigue Damage Process quickly with
The method of track frequency.
Background technology
When structure is subject to fatigue damage to destroy, the dynamic characteristic of structure will change correspondingly.Especially based on crackle
A series of appearance of damage status can cause the reduction of the rigidity of structure, so as to cause the modal parameter of structure, including intrinsic frequency,
Modal damping and modal parameters change, and change is also finally turned in the response for further resulting in structure generation.Many documents pair
Structure failure monitoring based on intrinsic frequency, Mode Shape etc. is studied.The reduction of wherein intrinsic frequency is easy to, so
Many fatigue damage researchs are namely based on this feature, and are paid close attention to be subject to many scholars.Many scholars are in some numerical methods
It is had begun in impact wave method with this detection means；At the same time, other scholars by load harmonic excitation come
Dynamic response is measured, fatigue damage phenomenon is studied by the changing features of dynamic response.
In the theoretical research of fatigue damage, A in 1847, which is irrigated time, proposes S-N Fatigue Life Curves and the fatigue damage limit
Concept has established some strength theory basis of fatigue damage destruction, is widest a kind of fatigue damage in current engineer application
Wound is theoretical；1963, P.C.Paris gave the famous relational expression of crack propagation law with the method for fracture mechanics ---
Paris formula, and developed " damage tolerance design "；Rabouthnov in 1963 proposes the concept of damage factor, 1977
Janson et al. proposes damage mechanics, by the development of decades, progressively develops the theoretical and microcosmic damage of continuum damage mechanics
Overstrain and theoretical based on microcosmic phenomenological damage becomes In Engineering Structural Damage and destroys weight with Study on Fatigue Life
Want mechanical analysis means.
It is proposed that " equivalent stiffness " is theoretical in nineteen ninety Krawczuk et al. various causes parameter to become show that crackle brings
The effect of change, so that studying a question becomes more simply and conveniently in method processing, and with the method for numerical simulation
Simulate the cantilever beam situation under different operating modes；Kim and Zhao carry out the crackle of detecting structure using harmonic response, and derive
Go out to have crack position depth to have the approximate equation of side slope effect of very strong susceptibility；Douka et al. is examined in the crackle of cantilever beam
The method that instantaneous frequency and classical mode decomposition have been used in survey, release instantaneous frequency variation and harmonic distortion increase all with
The crack depth of structure is related；Ruotolo et al. is judging that the crack size of cantilever beam and the research of position employs forced oscillation
Dynamic response；Pugno and Surace on different position have the cantilever beam of different size crackles in sinusoidal excitation for one in analysis
Under response when, used harmonic wave equilibrium method, it is found that the number of crackle, position and depth determine going out for higher hamonic wave on frequency spectrum
It is existing, and many times can be saved.
In the damage diagnosis based on modal parameter, many researchs have also been made in many scholars, propose many theoretical.1986
Walter and M.West proposes the damage position using Kind of Modal Confidence Factor (MAC) deagnostic structure.And A.J.Lieven and
D.J.Ewins proposes coordinate Kind of Modal Confidence Factor COMAC on the basis of MAC.Pandey in 1991 et al. proposes curvature
Mode Shape index, it is more more sensitive for damaging than MAC and COMAC.Yao in 1992 is proposed before being damaged by test structure
Modal strain energy variation afterwards carries out damage diagnosis.Pandey and Biswas is proposed based on test structure flexibility matrix within 1994
Damage diagnosis method.
Many researchs have been done in the influence that also there are many scholars in the country and cause structure dynamic response feature to fatigue damage.1993
Huang Dishan, Tong Zhifang, Sun Yueming et al. analyze crackle blade to rotor dynamic balancing and shake in faulty power mechanism is discussed
The influence of dynamic modulation.
It is also used using the Solution of Transfer Matrix crackle blade vibration characteristic by many scholars.Xu in 1997 can the fatigues such as monarch
The cantilever beam that cracks is damaged as calculated examples, analyzes the crack position of fatigue damage generation, depth to cantilever beam deflection
The influence of modal dynamic characteristic.The same year Xu Kejun etc. analyzes shadow of the crackle to blade mode of flexural vibration intrinsic frequency of two transverse directions
It rings, and finds that simple selection intrinsic frequency identifies Crack Parameters by analytical effect, it can underestimation severe crack degree；
Due to thinking that fatigue crack is exactly open-delta winding in most of researchs before, and it is research object with open-delta winding,
Folding without considering crackle acts on.So do excessively simplify fatigue crack, structure after fatigue damage can not be obtained
Real dynamic characteristic.The dynamic of cantilever beam of the method analysis with fatigue crack of Yang Haiyan transfer function matrix in 1999
Response.And with cosine function simulating crack folding situation, finally show that crackle not only results in the reduction of intrinsic frequency, Er Qiehui
Cause the nonlinear characteristic of forced vibration.
Currently, computer technology is showing improvement or progress day by day, the development that CAD, CAE technology are also advanced by leaps and bounds, various business's finite elements
Analysis software is increasingly ripe perfect, so that more and more scholars widely use CAE in actual research and work
Finite element analysis software.Using finite element method research fatigue damage phenomenon and fatigue damage is gone to exist to structure when at the same time
It is influenced in terms of modal parameter and dynamic response still less.But due to the raising of CAD and the technology of CAE software, it now is possible to
It carries out establishing physical model using structure of the CAD software with respect to fatigue damage, then model is imported into CAE finite element softwares,
Finite element analysis is further carried out, greatly improves analysis efficiency.
The content of the invention
The technical problems to be solved by the invention are in view of the foregoing drawbacks, to provide that the invention discloses a kind of fatigue damages
The method of quick tracking frequency in the process analyzes the frequency response function variation before and after structural damage, therefrom finds frequency response function variation
Relation between changing with intrinsic frequency, the method for realizing intrinsic frequency tracking is found with this.
The present invention uses following technical scheme to solve above-mentioned technical problem：
The method of quick tracking frequency in During Fatigue Damage Process, the method analyze the frequency response function change before and after structural damage
Change, therefrom find the relation between frequency response function variation and intrinsic frequency variation, the side for realizing intrinsic frequency tracking is found with this
Method.
Further, initially set up under experimental state by the multi-modes parameter of geodesic structure, encouraged, obtained with intrinsic frequency
The phase difference of input and output；After structural damage, in the case where excited frequency and amplitude are constant, and after one damage of acquisition
Phase difference；Then the corresponding frequency of current phase is found in original phase-frequency characteristic figure, then passes through phase-frequency characteristic and intrinsic frequency
Relational expression between rate obtains new intrinsic frequency；
If the new intrinsic frequency is unsatisfactory for Rule of judgment, using the new intrinsic frequency as input frequency,
It repeats the above process, obtains one group of new intrinsic frequency；By iterating, release by the intrinsic frequency of geodesic structure.
Further, the multi-modes parameter includes fixed frequency, damping ratio and phase-frequency characteristic.
Further, the frequency response function is：
Wherein, m1：First step mode quality；k1：First step mode rigidity；c1：First step mode damps f：Frequency；
Hij(f)：It is encouraged in j points, i points measure frequency response function during response；Xi(f)：The amplitude response function of i points；
Fj(f)：The exciting force function of j points；φi1：In the first step mode vibration shape of i points；
φj1:In the first step mode vibration shape of j points.
Further, the intrinsic frequency expression formula is：
fs=fn+f1-f2
Wherein, fs、fnFirst natural frequency and first natural frequency before damage after respectively damaging；f2For driving frequency, f1
For with reference to the identical Frequency point of driving frequency corresponding phase in phase-frequency characteristic curve.
The above method is applied to fatigue damage and tests the full stage.
As a preferred embodiment, this method further includes verification process, the verification process by phase-frequency characteristic curve
One section of curve is taken by intrinsic frequency, judge the phase of this section of curve and the difference between corresponding frequency and intrinsic frequency whether
In allowable range of error, if the intrinsic frequency that explanation in sight is measured by the method is real intrinsic frequency.
The present invention compared with prior art, has following technique effect using above technical scheme：
The frequency tracking method of phase-frequency characteristic, it spends lacks much on the time of frequency-tracking, so real to fatigue damage
It is negligible to test influence.It can realize automatic real-time track intrinsic frequency, alleviate the burden of experimenter, while the tracking of its method
Intrinsic frequency and the time spent in it is more accurate and more time saving than existing method respectively, so obtained result is also more accurate.
Description of the drawings
Fig. 1 is the amplitude-versus-frequency curve comparison diagram before and after structural damage；
Fig. 2 is the phase-frequency characteristic curve comparison figure before and after structural damage；
Fig. 3 is the frequency tracking method flow chart based on phase-frequency characteristic；
Fig. 4 is Euler-Bernoulli Jacob's beam finite element structural model；
The amplitude-versus-frequency curve figure of Fig. 5, Fig. 6 for structure in embodiment currently and after damage；
Fig. 7 is with reference to phase-frequency characteristic graph；
Fig. 8, Fig. 9, Figure 10 are the phase-frequency characteristic curve after damage in embodiment with referring to phase-frequency characteristic graph；
Figure 11 is the current amplitude-versus-frequency curve figure with after damage of structure in embodiment；
Figure 12 is with reference to phase-frequency characteristic graph；
Figure 13 is the phase-frequency characteristic curve after damage in embodiment with referring to phase-frequency characteristic graph.
Specific embodiment
Technical scheme is described in further detail below in conjunction with the accompanying drawings：
It realizes frequency-tracking, first has to the front and rear variation of research intrinsic frequency variation.Wherein especially frequency response function
Variation, because frequency response function includes the information of structured various parameters, the intrinsic frequency information including structure.
Frequency response function is there are many expression way, wherein common have amplitude-versus-frequency curve and phase-frequency characteristic curve.Such as Fig. 1 and
Shown in Fig. 2, when intrinsic frequency changes, the amplitude-versus-frequency curve and phase-frequency characteristic curve near intrinsic frequency are all become
Change, the variation of wherein phase-frequency characteristic curve is particularly evident.We can study this variation, therefrom accomplished frequency-tracking
Method.
In real modal analysis theory, N-dimensional has damping linear system vibration equation that can be expressed as：
Wherein, M, C, K are respectively the mass matrix, damping matrix and stiffness matrix of the system, x and the displacement that p is system
With suffered power.
Assuming that the vibration shape, modal mass, modal damping and the modal stiffness of system r ranks are respectively { φ }r、mr、crAnd kr,
By equation decoupling, diagonalization can obtain：
Assuming that the damping of system meets proportional damping, then damping can also carry out diagonalization,
C=α M+ β K (1.5)
Wherein, α, β are two damped coefficients of proportional damping.
These formulas are combined, and are write as matrix form, can be obtained：
ΦTM Φ=diag [m1...mr...mN] (1.7)
ΦTK Φ=diag [k1...kr...kN] (1.8)
ΦTC Φ=diag [c1...cr...cN] (1.9)
The mode superposition method responded using system, order
Wherein qr=Qejωt, substitute into vibration equation, and diagonalization：
Q=(- f2mrI+jfcrt+krI)-1ΦTP (1.11)
So the modal contribution factor of r ranks is：
It can thus be concluded that：
At this time if encouraged in j points, i points measure response, and frequency response function at this time is can obtain by (1.15) formula：
If ignore the interference of higher, and first-order modal, nearby without repetition, above formula can be reduced to：
Frequency-tracking based on phase-frequency characteristic
Phase-frequency characteristic is not often used compared with amplitude versus frequency characte in modal idenlification, reason be exactly phase-frequency characteristic for mould outside
Boundary's factor is very sensitive, and small variation may result in the variation of phase-frequency characteristic, this causes making an uproar for a little in real process
Acoustic jamming, which may result in surveyed phase-frequency characteristic, becomes inaccurate.Meanwhile phase-frequency characteristic variation is because structure has damping, still
Damping Theory is so far without complete theoretical system, and the damping of labyrinth is inherently influenced by factors, in reality
It is difficult to survey standard in itself during testing, let alone is applied in the Modal Parameter Identification of structure.
But undeniable is that phase-frequency characteristic is very sensitive to the variation of intrinsic frequency, this can know from Fig. 2
Road.How phase-frequency characteristic survey it is accurate in the case of, realize intrinsic frequency during structure fatigue damage using phase-frequency characteristic
Tracking just has great meaning.
The generation of phase is mainly frequency response function while includes real and imaginary parts.(1.17) formula is slightly changed and can be obtained：
By phase-frequency characteristic curve, that is, Fig. 2 and also assume that the phase difference at intrinsic frequency before and after structural damage is constant
Or error can be ignored, and can guess that the front and rear intrinsic frequency difference of its damage is equal to current excited frequency and exists with excited frequency
Phase difference after damage is in the difference with reference to corresponding frequency in phase-frequency characteristic graph.Following formula can be obtained：
fs=fn+f1-f2 (1.19)
According to formula (1.19) formula we just can known, initial modal idenlification and according to modal idenlification parameter
The parameter f being further calculatedn、f1、f2Substitute into, it is possible to obtain under current state intrinsic frequency fs。
The characteristics of this method is maximum is exactly quick, fn、f2It it is also known that, to be done for current excitations frequency as long as unique
Phase control reference phase-frequency characteristic curve obtains f according under current activation state1, substitute into formula (1.19) formula and calculate.It can
Certain preparation can be done before experiment, but compared with the frequency-tracking based on amplitude versus frequency characte, it during the experiment need not be substantial amounts of
Data, the time of frequency-tracking is also very short, so being exactly the later stage to experiment, frequency-tracking will not influence the tired of experiment
Labor damage process and the calculating of fatigue life.
Damping change is larger before and after some structural damages, may once cannot suitably intrinsic frequency using the above method
Rate, so when the intrinsic frequency calculated when first time is unsatisfactory for decision condition, we use the intrinsic frequency newly obtained again
Into row energization, and the corresponding frequency in reference phase-frequency characteristic graph of the phase under encouraging at this time is obtained, then again with above-mentioned
Method is calculated, and is iterated by doing so until acquisition meets the intrinsic frequency of decision condition.
In order to reduce error, several Frequency points can be looked for obtain multiple equations into row energization more.It thus obtains based on phase
The second method of the frequency-tracking of frequency characteristic.
This method is compared compared with former is based on the frequency tracking method of phase-frequency characteristic, opposite to need more number
According to solving, but compared with the frequency-tracking based on amplitude versus frequency characte, required data are relatively also many less, needed for frequency-tracking
Time is not grown, in contrast, exactly arrived experiment later stage, frequency-tracking will not influence experiment During Fatigue Damage Process and
The calculating of fatigue life.
With reference to two kinds based on phase-frequency characteristic frequency tracking method, consider, the frequency tracking method based on phase-frequency characteristic
It is final sum up for：The required equation number N (N >=2) of second method is determined first, is encouraged with current frequency, is obtained a phase
Position, according to first method, is calculated new frequency, then with new frequency excitation structure, with reference to basis for estimation, judgement is
It is not real structural natural frequencies.If it is, explanation has found；If it is not, then one group of data is obtained, then with new frequency
Excitation, obtains a phase, according to first method, new frequency is calculated, then with new frequency excitation structure, with reference to sentencing
Disconnected foundation judges to be real structural natural frequencies.And so on, when after n times, obtaining required N group data, use
This second method calculates, and obtains intrinsic frequency.It can certainly be judged with previous basis for estimation.Specific such as block diagram 3
It is shown.
Embodiment
Harmonic responding analysis when the present embodiment is by using Euler-Bernoulli Jacob's beam progress model configuration forced vibration, ratio resistance
Buddhist nun also will allow in the oscillatory differential equation of system, and the feasibility of intrinsic frequency tracking is verified with this.
By girder construction discretization, consider further that the structural vibration differential equation after damping is：
[M] is mass matrix in formula, and [K] is the stiffness matrix for not damaging girder construction, the two matrixes can have unit
Mass matrix and element stiffness matrix are composed, and [C] is not damage the damping matrix of girder construction, and { P (t) } applies to be external
Force vector, { q (t) } respond for node.The damping of girder construction can be set to proportional damping, therefore the damping matrix of girder construction can be with
It is write as：
[C]=α [M]+β [K] (2.2)
α in formula, β are two damped coefficients of proportional damping, are rayleigh quotient damping factors.
By given boundary condition, [M], [C] and [K] and amplitude of exciting force { P } can calculate the Harmony response of unit
Some initial mode supplemental characteristics of value and girder construction.
The relation of damping ratio and intrinsic frequency can be expressed as：
ξ in formulanFor damping ratio, fnFor intrinsic frequency.It can if two intrinsic frequencies of known structure and its corresponding damping ratio
To draw following equation：
So α and β can be acquired by formula (2.5)：
F in formulamAnd fnIt is system low order and the intrinsic frequency of high-order.
Structural damage does not interfere with the qualitative character of structure, but the stiffness characteristics to structure and damping characteristic generation one usually
Fixed influence.The only rigidity of influence blade and damping, therefore the vibration equation for damaging back beam structure is are assumed during damage：
Subscript c represents damage, { q in formulac(t) } be damage after node response, [Kc] for damage after stiffness matrix,
[Cc] for damage after damping matrix.
Unit damages, and the stiffness matrix of unit is caused to damage so that the stiffness matrix for damaging unit changes, with new
Element stiffness matrix after damage replaces original element stiffness matrix, and new rigidity is formed together with other element stiffness matrixs
Matrix, that is, the stiffness matrix [K after damagingc]。
But cannot be formed compared with damping battle array with such method, because proportional damping theory is suitable only for structure
It is whole, it is not suitable for a certain unit of structure.So as the variation of damping, two proportionality coefficients can also occur therewith after damage
Variation, but situation about changing is unknown.So new proportionality coefficient is only led to the intrinsic frequency after damage and damping ratio
Formula (2.5) solution is crossed to obtain.For convenience's sake, we use αcAnd βcRepresent the proportionality coefficient of structure after damaging.After so damaging
The damping matrix of girder construction can be write as：
[Cc]=αc[M]+βc[Kc] (2.7)
Wherein αcAnd βcBecause the difference of degree of impairment has different variations, we on the basis of α and β respectively to become
It is emulated exemplified by changing ± 10%, ± 20%, ± 30% and ± 50%.
Given boundary condition, [M], [C] and [K] and amplitude of exciting force { P } can calculate the Harmony response value of unit.
Emulation establishes finite element model with Euler-Bernoulli Jacob's beam, divides finite element unit, establishes element mass matrix and list
First stiffness matrix, thus form girder construction total quality matrix and Bulk stiffness matrix, and with the damping proportional coefficient of setting
The integral damping matrix of girder construction is calculated.In conjunction with given exciting force come the frequency of simulation architecture During Fatigue Damage Process with
Track.
It is established with girder construction shown in Fig. 4 and divides finite element model, the basic parameter of beam has：E=70GPa, L=100cm,
g/cm3, A=2cm*2cm, α=0.1, β=10-5.Beam is equidistantly divided into ten finite element units.
For a certain unit, ignore the axial vibration of beam, the shape function of girder construction can be expressed as：
Thus the geometric matrix of beam element is obtained：
The mass matrix and stiffness matrix of ejector unit：
With element mass matrix and element stiffness matrix, the total quality matrix and Bulk stiffness matrix of girder construction are formed.
With reference to boundary condition, i.e. beam left end is fixed, and it is 103.56Hz and 647.76Hz tentatively to obtain the one of beam, second order intrinsic frequency.This
Illustrate that beam does not have repetition, and the intrinsic frequency interval of one or two this adjacent two rank is farther out.Corresponding damping ratio is 0.002 He
0.0066, in (2.5) formula, α=0.098, β=0.99 × 10 are calculated-5
Structural damage can cause the rigidity of structure to reduce, and from the angle of finite element unit, exactly damage the bullet of unit
Property modulus reduces.Assuming that Unit the 5th of girder construction damages, elasticity modulus is reduced to E'=50GPa by E=70GPa,
Remaining parameter constant.Element stiffness matrix is so substituted into, obtains the stiffness matrix of damage unit：
And damage element stiffness matrix is replaced into original stiffness matrix, form new Bulk stiffness matrix.With reference to entirety
Mass matrix and boundary condition, the first natural frequency to damage back beam structure of calculating is 99.89Hz.
In the case where damaging both front and back state, reinforced in No. 10 unit right ends, while No. 4 and No. 5 unit contact positions of measurement
Response, and responded with this divided by power obtains Harmony response at this time, and analyze the feasibility for verifying frequency-tracking.
The basic ideas of frequency tracking method based on phase-frequency characteristic be with the intrinsic frequency of current structure into row energization, when
When the current phase-frequency characteristic of monitoring of structures phase value, and using phase value as normative reference, when phase value generate it is a degree of
During variation, the reference phase-frequency characteristic measured before starting with experiment compares, and finds corresponding with same phase under current excitations frequency
Frequency, with reference to other modal parameters, the intrinsic frequency after structural damage is calculated, and using this frequency as consolidating after variation
There is frequency to continue to encourage.
When phase-frequency characteristic curve when this method will measure structure most initial before the experiments is tracked as subsequent frequencies
Reference frame, as shown in figure 11.It is -91.0312 ° with reference to phase of the phase-frequency characteristic curve at intrinsic frequency 103.56Hz,
In addition frequency be at 103.54Hz, 103.55Hz, 103.57Hz and 103.58Hz corresponding phase for -79.0748 °, -
84.4876 °, -95.5119 ° and -100.9231 °, it is contemplated that the number of significant digit problem of calculated value, when the frequency pair being calculated
For the phase value answered between -80 ° and -100 °, that is, it is new intrinsic frequency to think the frequency.
The generation of phase is because there is damping in structure, and the size of damping influences whether phase value, so
Different αcAnd βcMeeting generate different phase-frequency characteristic curves, so causing the frequency based on phase-frequency characteristic to different phase-frequency characteristics
Some difference on tracking.
It chooses than more typical αcAnd βc, it is corresponding to generate several phase-frequency characteristic curves, with reference to phase-frequency characteristic curve is referred to, have
The feasibility of frequency tracking method of the experience card based on phase-frequency characteristic.
Work as αc=0.12 and βcWhen=0.000012, phase-frequency characteristic curve and phase-frequency characteristic reference curve figure after damage are such as
Shown in Fig. 8.Assuming that current excitations frequency is 100Hz, the 103.67Hz in -137.7451 ° of phase, with phase-frequency characteristic reference curve
The phase at place approaches.So with the first method of the frequency-tracking based on phase-frequency characteristic, parameter f at this timen=103.56Hz, f1
=103.67Hz, f2=100Hz substitutes into formula (1.19) formula, and f is calculateds=99.8940Hz, with theoretical value 99.89Hz basic one
It causes.
Work as αc=0.08 and βcWhen=0.000007, phase-frequency characteristic curve and phase-frequency characteristic reference curve figure after damage are such as
Shown in Fig. 9.The same with the above method, but pass through and calculate, the intrinsic frequency of obtained structure is unsatisfactory for judging requirement, Gu again into
Row method two calculates, and iteration once obtains the intrinsic frequency for meeting determination requirement.Detailed process is as shown in table 1.
15 secondary frequencies of table track calculating process experimental result table
fs=103.56+100-103.71=99.85Hz (2.13)
By iteration once after obtain：
fs=103.56+99.85-103.5=99.91Hz (2.14)
Equation group is solved to obtain：fs=99.91Hz
Work as αc=0.15 and βcWhen=0.000015, phase-frequency characteristic curve and reference phase-frequency characteristic figure such as Figure 10 after damage
It is shown.It is the same with the above method, but calculate, the intrinsic frequency of structure is not obtained, detailed process is as shown in table 2.
At this point, just with the second method of the frequency-tracking based on phase-frequency characteristic.
25 secondary frequencies of table track calculating process experimental result table
fs=103.56+100-103.64=99.92Hz (2.15)
fs=103.56+99.92-103.51=99.98Hz (2.16)
fs=103.56+99.98-103.63=99.91Hz (2.17)
：fs=99.91Hz
As can be seen that the frequency tracking method based on amplitude versus frequency characte and phase-frequency characteristic is all feasible from numerical simulation situation
, but simultaneously it also seen that some do not have the problem in theory analysis in concrete numerical value simulation, it is main to embody a concentrated reflection of
After two damped coefficient changes, a degree of variation also has occurred in frequency response function.
Amplitude versus frequency characte is smoothened with the increase of damping near intrinsic frequency, becomes steep with the reduction of damping
It is high and steep, but the maximum point during amplitude remains this section of bandwidth at the intrinsic frequency.So the variation of damping is to being based on amplitude-frequency spy
Property frequency-tracking influence it is little.
But damping change based on the frequency tracking method of phase-frequency characteristic with regard to different, but damping change is little, as long as
The intrinsic frequency after can just being damaged substantially is once calculated with the frequency-tracking first method based on phase-frequency characteristic, still
When changing greatly, because the difference of variation, is difficult to be damaged with the frequency tracking method first method based on phase-frequency characteristic
Intrinsic frequency after wound.
New frequency larger when damping, and when with the first method of the frequency tracking method based on phase-frequency characteristic, obtaining
Rate data scatter, with new frequency excitation structure, but obtained phase but can not find on reference to phase-frequency characteristic curve it is corresponding
Frequency, i.e., not in phase-frequency characteristic curve ranges.If data at this time do not reach the value N of setting also, can be with fs=f1-fn+
f2It substitutes into and continues iteration.Intrinsic frequency of this value after fatigue damage starting stage infinite approach and damage, with this formula
It can also be used as empirical equation in the starting stage, intrinsic frequency be calculated so as into line trace.
By discussion earlier herein, the method for finding realization intrinsic frequency tracking during structure fatigue damage experiment,
Relevant foundation is found for the research and design of structure fatigue damage long run test, Harmony response before and after damaging occurs by girder construction
Analysis demonstrates the feasibility of frequency tracking method.This chapter will focus on introduction and further be verified in structure by specific experiment
The feasibility of intrinsic frequency tracking is realized in fatigue damage long run test.
Experiment content
Experiment purpose is to verify the feasibility of intrinsic frequency tracking, then must have the number before and after structural damage
According to so to distinguish measurement structure in the front and rear data of damage.Measurement data is mainly before and after structural damage near intrinsic frequency
The frequency response function that frequency sweep obtains, including amplitude-versus-frequency curve and phase-frequency characteristic curve.In addition ratio resistance is used in experimental verification
Two the proportionality coefficients α and β of Buddhist nun, so also to measure the intrinsic frequency and damping ratio of a second order.
In order to realize experiment purpose, equipment needed for experiment has：NI USB-4431 data collectors, MA-600 power amplifiers, ICP
Acceleration transducer, NES-1 type eddy-current exciters.The basic process of experiment is：Signal source one end is connected to computer, soft by computer
Part control signal source exports, another to terminate to power amplifier, then by power amplifier and NES-1 type eddy-current exciter phases
Even；ICP acceleration transducers are accompanied into the chucking surface of blade with two-sided be adhesive in；ICP acceleration transducers and signal source
Signal be wired to NI4431 data collectors, NI4431 data collectors are coupled to computer, with software collection data
And it is analyzed.
Simple introduction is done to the instrument used in experiment below.
Signal source：Various required signals can be generated, are exported as electronic signals.The signal magnitude of signal source output
It is controlled by with frequency by signal source control software.The electric signal that signal source generates is generally smaller, to pass through power amplifier
It could be used after amplification.
Power amplifier：The principle amplified with circuit, will be amplified by the electric signal of power amplifier, has been reached
The standard of vibrator movement can be evoked.
NES-1 eddy-current exciters：Basic principle is switched on generating current vortex, current vortex under conducting wire and magnetic field collective effect
Drive test specimen vibration.
NI4431 data collectors：The data collector of NI companies of U.S. production, is connected with USB interface with computer, and
Different programs can be write according to the needs of user itself, there is stronger analysis, research function.
ICP acceleration transducers：The acceleration amplifier of built-in integrated circuit, by traditional acceleration transducer and external
The sensor that preamplifier is made of one.The influence that connecting cable is brought can be eliminated.
By experiment, the second order intrinsic frequency measured before damage is respectively 1109Hz and 2308Hz, and one at identification
The damping ratio of second order is respectively 0.0209 and 0.0097, substitutes into (2.3) formula, obtains：
It solves：
Assuming that the intrinsic frequency of current structure is 1109Hz, from the current amplitude-versus-frequency curve with after damage of structure of Figure 11
0.01176 when the upper amplitude that can see at 1109Hz is by resonating is reduced to 0.01144 after damage, apparent width occurs
Value variation.So with amplitude as basis for estimation, when amplitude changes a lot, frequency sweep is carried out in a small range, is damaged
Amplitude-versus-frequency curve afterwards finds out the maximum point of the amplitude-versus-frequency curve, and intrinsic as after damaging using the frequency of the point
Frequency, then frequency-tracking is realized into row energization with the frequency.The characteristic maximum of amplitude-frequency after damaging is found in this approach
Point, frequency 1101Hz.It is achieved thereby that intrinsic frequency tracks.
When phase-frequency characteristic curve when this method will measure structure most initial before the experiments is tracked as subsequent frequencies
Reference frame, as shown in figure 12.It it is 143.63916 ° with reference to phase of the phase-frequency characteristic at intrinsic frequency 1109Hz, in addition frequently
Rate be at 1107Hz, 1108Hz, 11110Hz and 1111Hz corresponding phase be 139.041458 °, 141.455109 °,
146.130295 ° and 148.938019 °, it is contemplated that the number of significant digit problem of calculated value, when the corresponding phase of the frequency being calculated
For place value between -140 ° and -148 °, that is, it is new intrinsic frequency to think the frequency.
Phase-frequency characteristic curve and phase-frequency characteristic reference curve figure after damage is as shown in figure 13.Assuming that current excitations frequency is
1109Hz, the phase at 1017Hz in -137.7451 ° of phase, with phase-frequency characteristic reference curve approach.So with based on phase frequency
The first method of the frequency-tracking of characteristic, at this time parameter fn=1109Hz, f1=1117Hz, f2=1109Hz, α=47.7648
With β=- 5.637 × 10-7(1.24) formula of substitution, is calculated fs=1100.598Hz, it is basically identical with theoretical value 1101Hz.
Because experimental data is limited, by certain calculating for several times still without obtaining the intrinsic frequency situation of structure
Occur, specific data are as shown in table 3.
3 secondary frequencies of table track calculating process
fs=1109+1109-1117=1101Hz (3.3)
It solves：fs=1101Hz, it is consistent with experiment data measured.
By numerical simulation and experimental data away from verification, the feasibility of both intrinsic frequency trackings is all demonstrated.
So the scheme of blade fatigue injury experiment can be designed based on this：
1. prepare before experiment.Initial substantially experiment obtains the approximate range of Natural Frequency of Blade before experiment, then herein
In the range of be compared careful frequency sweep, measuring a certain measuring point of blade, (amplitude versus frequency characte is bent for the Frequency Response of signal source signal
Line obtains simultaneously), find the exact natural frequency value of blade.According to different intrinsic frequency trackings, different ginsengs is selected
Examining standard, (intrinsic frequency based on amplitude versus frequency characte tracks corresponding normative reference as amplitude, and the intrinsic frequency based on phase-frequency characteristic
It is phase that rate, which tracks corresponding normative reference), setting think blade fatigue damage occurs and tempers two kinds in the case of with reference to ginseng
The limit of number variation.
2. the driving frequency of signal source is set to the current intrinsic frequency of blade, the increasing of Regulate signal source level and power amplifier
Benefit so that the corresponding measuring point of blade reaches the amplitude of setting, fixed frequency excitation blade.Hereafter ensure that the gain of power amplifier no longer changes
Become.
3. it is considered as blade once the variation of fatigue damage setting degree occurs when reference parameter and fatigue damage occurs, Gu
There is frequency also to change therewith, new intrinsic frequency is traced into using corresponding intrinsic frequency tracking.With new intrinsic
Frequency encourages blade, then Regulate signal source level for the fixed frequency of driving frequency so that the corresponding measuring point of blade reaches the amplitude of setting
Value, continues to test.
4. when the variation more than fracture setting degree occurs for reference parameter, it is believed that blade is broken, and terminates experiment.
Above-described specific embodiment has carried out the purpose of the present invention, technical solution and advantageous effect further
It is described in detail, it should be understood that the foregoing is merely the specific embodiments of the present invention, is not limited to this hair
Bright, within the spirit and principles of the invention, any modification, equivalent substitution, improvement and etc. done should be included in the present invention
Protection domain within.
Claims (7)
1. the method for quick tracking intrinsic frequency during fatigue test of structure, which is characterized in that the method analysis structure damage
The front and rear frequency response function variation of wound, therefrom finds the relation between frequency response function variation and intrinsic frequency variation, reality is found with this
The method of existing intrinsic frequency tracking.
2. the method for quick tracking intrinsic frequency during fatigue test of structure according to claim 1, which is characterized in that
The method is specially：It initially sets up under experimental state by the multi-modes parameter of geodesic structure, is encouraged, obtained defeated with intrinsic frequency
Enter the phase difference with output；After structural damage, in the case where excited frequency and amplitude are constant, and the phase after a damage is obtained
Potential difference；Then the corresponding frequency of current phase is found in original phase-frequency characteristic figure, then passes through phase-frequency characteristic and intrinsic frequency
Between relational expression, obtain new intrinsic frequency；
If the new intrinsic frequency is unsatisfactory for Rule of judgment, using the new intrinsic frequency as input frequency, repeat
The above process obtains one group of new intrinsic frequency；By iterating, release by the intrinsic frequency of geodesic structure.
3. the method for quick tracking frequency in During Fatigue Damage Process according to claim 2, which is characterized in that described multistage
Modal parameter includes fixed frequency, damping ratio and phase-frequency characteristic.
4. the method for quick tracking frequency in During Fatigue Damage Process according to claim 2, which is characterized in that the frequency response
Function is：
<mrow>
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<mo>=</mo>
<mfrac>
<mrow>
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<mi>X</mi>
<mi>i</mi>
</msub>
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<mi>f</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>F</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&phi;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
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<mi>&phi;</mi>
<mrow>
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<mn>1</mn>
</mrow>
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</mrow>
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</msup>
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Wherein, m1：First step mode quality；k1：First step mode rigidity；c1：First step mode damps f：Frequency；
Hij(f)：It is encouraged in j points, i points measure frequency response function during response；Xi(f)：The amplitude response function of i points；
Fj(f)：The exciting force function of j points；φi1：In the first step mode vibration shape of i points；
φj1:In the first step mode vibration shape of j points.
5. the method for quick tracking frequency in During Fatigue Damage Process according to claim 2, which is characterized in that described intrinsic
Frequency expression is：
fs=fn+f1-f2
Wherein, fs、fnFirst natural frequency and first natural frequency before damage after respectively damaging；f2For driving frequency, f1For ginseng
Examine the Frequency point that driving frequency corresponding phase is identical in phase-frequency characteristic curve.
6. the method for quick tracking frequency in During Fatigue Damage Process according to claim 5, which is characterized in that this method should
The full stage is tested for fatigue damage.
7. the method for quick tracking frequency in During Fatigue Damage Process according to claim 6, which is characterized in that this method is also
Including verification process, the verification process judges this by taking one section of section near intrinsic frequency on phase-frequency characteristic curve
Whether the difference between the corresponding frequency of phase and intrinsic frequency of one section of curve is in allowable range of error, if explanation in sight is logical
It is real intrinsic frequency to cross the intrinsic frequency that the method measures.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109342572A (en) * | 2018-11-30 | 2019-02-15 | 中国航空工业集团公司沈阳飞机设计研究所 | A kind of outfield plane airfoil honeycomb corrosion damage lossless detection method and system |
-
2017
- 2017-11-30 CN CN201711235062.0A patent/CN108106826A/en active Pending
Non-Patent Citations (1)
| Title |
|---|
| 徐向泽: "结构疲劳试验中频率跟踪方法研究", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109342572A (en) * | 2018-11-30 | 2019-02-15 | 中国航空工业集团公司沈阳飞机设计研究所 | A kind of outfield plane airfoil honeycomb corrosion damage lossless detection method and system |
| CN109342572B (en) * | 2018-11-30 | 2022-02-22 | 中国航空工业集团公司沈阳飞机设计研究所 | Nondestructive testing method and system for corrosion damage of outfield airplane airfoil honeycomb structure |
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